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On Well-Posedness of Semilinear Stochastic Evolution Equations on L_p Spaces

Marinelli, C; (2018) On Well-Posedness of Semilinear Stochastic Evolution Equations on L_p Spaces. SIAM - Journal on Mathematical Analysis , 50 (2) pp. 2111-2143. 10.1137/16M108001X. Green open access

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Abstract

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L_p$ spaces, driven by multiplicative Wiener noise, with a drift term given by a superposition operator that is assumed to be quasi-monotone and polynomially growing, but not necessarily continuous. In particular, we consider a notion of mild solution ensuring that the superposition operator applied to the solution is still function-valued but satisfies only minimal integrability conditions. The proofs rely on stochastic calculus in Banach spaces, monotonicity and convexity techniques, and weak compactness in L_1 spaces.

Type: Article
Title: On Well-Posedness of Semilinear Stochastic Evolution Equations on L_p Spaces
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/16M108001X
Publisher version: https://doi.org/10.1137/16M108001X
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, stochastic PDEs, monotone operators, convex analysis, REACTION-DIFFUSION EQUATIONS, BANACH-SPACES, WEAK SOLUTIONS, EXISTENCE, NOISE
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1557459
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